Wavelets and Singular Integrals on Curves and Surfaces
David, Guy.
Wavelets and Singular Integrals on Curves and Surfaces [electronic resource] / by Guy David. - X, 110 p. online resource. - Nankai Institute of Mathematics, Tianjin, P.R. China ; 1465 . - Nankai Institute of Mathematics, Tianjin, P.R. China ; 1465 .
Wavelets -- Singular integral operators -- Singular integrals on curves and surfaces.
Wavelets are a recently developed tool for the analysis and synthesis of functions; their simplicity, versatility and precision makes them valuable in many branches of applied mathematics. The book begins with an introduction to the theory of wavelets and limits itself to the detailed construction of various orthonormal bases of wavelets. A second part centers on a criterion for the L2-boundedness of singular integral operators: the T(b)-theorem. It contains a full proof of that theorem. It contains a full proof of that theorem, and a few of the most striking applications (mostly to the Cauchy integral). The third part is a survey of recent attempts to understand the geometry of subsets of Rn on which analogues of the Cauchy kernel define bounded operators. The book was conceived for a graduate student, or researcher, with a primary interest in analysis (and preferably some knowledge of harmonic analysis and seeking an understanding of some of the new "real-variable methods" used in harmonic analysis.
9783540463771
10.1007/BFb0091544 doi
Mathematics.
Global analysis (Mathematics).
Functional analysis.
Topological Groups.
Applications of Mathematics.
Analysis.
Functional Analysis.
Topological Groups, Lie Groups.
Real Functions.
T57-57.97
519
Wavelets and Singular Integrals on Curves and Surfaces [electronic resource] / by Guy David. - X, 110 p. online resource. - Nankai Institute of Mathematics, Tianjin, P.R. China ; 1465 . - Nankai Institute of Mathematics, Tianjin, P.R. China ; 1465 .
Wavelets -- Singular integral operators -- Singular integrals on curves and surfaces.
Wavelets are a recently developed tool for the analysis and synthesis of functions; their simplicity, versatility and precision makes them valuable in many branches of applied mathematics. The book begins with an introduction to the theory of wavelets and limits itself to the detailed construction of various orthonormal bases of wavelets. A second part centers on a criterion for the L2-boundedness of singular integral operators: the T(b)-theorem. It contains a full proof of that theorem. It contains a full proof of that theorem, and a few of the most striking applications (mostly to the Cauchy integral). The third part is a survey of recent attempts to understand the geometry of subsets of Rn on which analogues of the Cauchy kernel define bounded operators. The book was conceived for a graduate student, or researcher, with a primary interest in analysis (and preferably some knowledge of harmonic analysis and seeking an understanding of some of the new "real-variable methods" used in harmonic analysis.
9783540463771
10.1007/BFb0091544 doi
Mathematics.
Global analysis (Mathematics).
Functional analysis.
Topological Groups.
Applications of Mathematics.
Analysis.
Functional Analysis.
Topological Groups, Lie Groups.
Real Functions.
T57-57.97
519